The police would never tell a citizen to speed

The police would never tell a citizen to speed, even in an emergency situation. A non-emergency vehicle speeding is incredibly dangerous, and can result in death, since there are no sirens, and the driver hasn't been trained. But it's particularly ridiculous in this movie, since it wasn't even an emergency situation. Jennifer was already in hospital. Speeding would have absolutely no impact on her condition. And since it wasn't an emergency situation, the police couldn't speed, or use their sirens.